Problem: Multiply the following complex numbers: $({-3-i}) \cdot ({-1-5i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3-i}) \cdot ({-1-5i}) = $ $ ({-3} \cdot {-1}) + ({-3} \cdot {-5}i) + ({-1}i \cdot {-1}) + ({-1}i \cdot {-5}i) $ Then simplify the terms: $ (3) + (15i) + (1i) + (5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 3 + (15 + 1)i + 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 3 + (15 + 1)i - 5 $ The result is simplified: $ (3 - 5) + (16i) = -2+16i $